{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:41:01Z","timestamp":1787323261766,"version":"build-2736575974"},"reference-count":10,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>It is shown that under standard hypotheses, if stochastic approximation iterates remain tight, they converge with probability one to what their o.d.e. limit suggests. A simple test for tightness (and therefore a.s. convergence) is provided. Further, estimates on lock-in probability, i.e., the probability of convergence to a specific attractor of the o.d.e. limit given that the iterates visit its domain of attraction, and sample complexity, i.e., the number of steps needed to be within a prescribed neighborhood of the desired limit set with a prescribed probability, are also provided. The latter improve significantly upon existing results in that they require a much weaker condition on the martingale difference noise.<\/jats:p>","DOI":"10.1137\/090769363","type":"journal-article","created":{"date-parts":[[2010,10,26]],"date-time":"2010-10-26T18:06:13Z","timestamp":1288116373000},"page":"5178-5192","source":"Crossref","is-referenced-by-count":14,"title":["On the Convergence, Lock-In Probability, and Sample Complexity of Stochastic Approximation"],"prefix":"10.1137","volume":"48","author":[{"given":"Sameer","family":"Kamal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,10,26]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"A. Benveniste, M. M\u00e9tivier, and P. Priouret,\n                      Adaptive Algorithms and Stochastic Approximation\n                      , Springer-Verlag, Berlin, 1990.","DOI":"10.1007\/978-3-642-75894-2"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548301004953"},{"key":"R3","unstructured":"V. S. Borkar,\n                      Stochastic Approximation: A Dynamical Systems Viewpoint\n                      , Hindustan Publ. Co., New Delhi, and Cambridge University Press, Cambridge, UK, 2008."},{"key":"R4","unstructured":"H.F. Chen,\n                      Stochastic Approximation and Its Applications\n                      , Nonconvex Optim. Appl. 64, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002."},{"key":"R5","first-page":"59","volume":"35","author":"Derevitskii D. P.","year":"1974","journal-title":"Automat. Remote Control"},{"key":"R6","unstructured":"M. Duflo,\n                      Random Iterative Models\n                      , Appl. Math. (N.Y.) 34, Springer-Verlag, Berlin, 1997."},{"key":"R7","unstructured":"H. J. Kushner and G. G. Yin,\n                      Stochastic Approximation and Recursive Algorithms and Applications\n                      , 2nd ed., Appl. Math. (N.Y.) 35, Springer-Verlag, New York, 2003."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1977.1101561"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729586"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"H. Walk,\n                      Foundations of stochastic approximation\n                      , in Stochastic Approximation and Optimization of Random Systems, L. Ljung, G. Pflug, and H. Walk, eds., Birkh\u00e4user-Verlag, Basel, 1992.","DOI":"10.1007\/978-3-0348-8609-3_1"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090769363","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:51:23Z","timestamp":1787320283000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090769363"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":10,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090769363"],"URL":"https:\/\/doi.org\/10.1137\/090769363","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}